This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A338883 #12 Jul 03 2022 13:56:18 %S A338883 1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,18,20,21,22,24,28,30,33,35,36,40, %T A338883 42,44,45,48,55,56,60,63,66,70,72,77,80,84,90,99,105,110,112,120,126, %U A338883 132,140,144,154,165,168,180,198,210,231,240,252,280,315,330,336,360,420,462,495,504,630,720,840,990,1260 %N A338883 Orders of elements of the Rubik's Cube group. %C A338883 The Rubik's Cube group G is a subgroup of the symmetric group S_48 of order |G| = 43252003274489856000 = 2^27 * 3^14 * 5^3 * 7^2 * 11, generated by the six face twists of the cube. The elements of G have 73 distinct orders. The exponent of G, given by the least common multiple of the orders of the elements, is 55440. %H A338883 Jaap's Puzzle Page, <a href="https://www.jaapsch.net/puzzles/cubic3.htm#p34">Order of elements</a>, Cubic Circular, Issue 3 & 4, Spring & Summer 1982, p 34. %e A338883 10 is in the sequence because the algorithm U R U' F2 (in Singmaster notation) has order 10. %e A338883 13 is not in the sequence because 13 is a prime not dividing the order of the group. %Y A338883 Cf. A075152, A330389. %Y A338883 Number of elements of order a(n): A339122. %K A338883 nonn,fini,full %O A338883 1,2 %A A338883 _Ben Whitmore_, Nov 13 2020